The Linear Time Frequency Analysis Toolbox is a MATLAB/Octave toolbox for computational time-frequency analysis. It is intended both as an educational and computational tool. The toolbox provides the basic Gabor, Wilson and MDCT transform along with routines for constructing windows (filter prototypes) and routines for manipulating coefficients. It also provides a bunch of demo scripts devoted either to demonstrating the main functions of the toolbox, or to exemplify their use in specific signal processing applications. In this paper we describe the used algorithms, their mathematical background as well as some signal processing applications.